Is it standard when creating a 3D game model to only use one mesh?
Copying a couple performance tips from this thread —


Reuse geometries and materials whenever possible
Use instanced geometries for faster mesh instantiations
Merge meshes when possible


The main thing is that the more meshes and materials you have, the more draw calls you are making to the GPU, and you'll get worse performance than if you were drawing the same number of triangles using fewer meshes. Performance considerations in e.g. Unity may be a bit different, where the engine is probably optimizing your model somewhat for you.

If you're having issues exporting animation, that's probably unrelated: there are a fair number of open bugs about animation in the three.js Blender exporter. May have better luck exporting FBX or glTF (with either of KhronosGroup/glTF-Blender-Exporter or Kupoman/blender2gltf) before loading in three.js.